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Time series forecasting and spatiotemporal kriging are the two most important tasks in spatiotemporal data analysis. Recent research on graph neural networks has made substantial progress in time series forecasting, while little attention has been paid to the kriging problem---recovering signals for unsampled locations/sensors. Most existing scalable kriging methods (e.g., matrix/tensor completion) are transductive, and thus full retraining is required when we have a new sensor to interpolate. In this paper, we develop an Inductive Graph Neural Network Kriging (IGNNK) model to recover data for unsampled sensors on a network/graph structure. To generalize the effect of distance and reachability, we generate random subgraphs as samples and the corresponding adjacency matrix for each sample. By reconstructing all signals on each sample subgraph, IGNNK can effectively learn the spatial message passing mechanism. Empirical results on several real-world spatiotemporal datasets demonstrate the effectiveness of our model. In addition, we also find that the learned model can be successfully transferred to the same type of kriging tasks on an unseen dataset. Our results show that: 1) GNN is an efficient and effective tool for spatial kriging; 2) inductive GNNs can be trained using dynamic adjacency matrices; 3) a trained model can be transferred to new graph structures and 4) IGNNK can be used to generate virtual sensors.

AAAI 2021

Inductive Graph Neural Networks for Spatiotemporal Kriging

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INTERMAG 2021

technical paper

The purpose of the AAAI conference is to promote research in artificial intelligence (AI) and scientific exchange among AI researchers, practitioners, scientists, and engineers in affiliated disciplines. 

In continuing tasks, average-reward reinforcement learning may be a more appropriate problem formulation than the more common discounted reward formulation. As usual, learning an optimal policy in this setting typically requires a large amount of training experiences. Reward shaping is a common approach for incorporating domain knowledge into reinforcement learning in order to speed up convergence to an optimal policy. However, to the best of our knowledge, the theoretical properties of reward shaping have thus far only been established in the discounted setting. This paper presents the first reward shaping framework for average-reward learning and proves that, under standard assumptions, the optimal policy under the original reward function can be recovered. In order to avoid the need for manual construction of the shaping function, we introduce a method for utilizing domain knowledge expressed as a temporal logic formula. The formula is automatically translated to a shaping function that provides additional reward throughout the learning process. We evaluate the proposed method on three continuing tasks. In all cases, shaping speeds up the average-reward learning rate without any reduction in the performance of the learned policy compared to relevant baselines.

Temporal-Logic-Based Reward Shaping for Continuing Reinforcement Learning Tasks

AI practitioners typically strive to develop the most  accurate systems,  making an implicit assumption that the AI system will function autonomously. However, in practice, AI systems often are used to provide advice to people in domains ranging from criminal justice and finance to healthcare. In such AI-advised decision making, humans and machines form a team, where the human is responsible for making final decisions.   But is the most accurate AI the best teammate? We argue "not necessarily" --- predictable performance may be worth a slight sacrifice in AI accuracy. Instead, we argue that AI systems should be trained in a human-centered manner, directly optimized for team performance. We study this proposal for a specific type of human-AI teaming, where the human overseer chooses to either accept the AI recommendation or solve the task themselves. To optimize the team performance for this setting we maximize the team's expected utility, expressed in terms of the quality of the final decision, cost of verifying, and individual accuracies of people and machines. Our experiments with linear and non-linear models on real-world, high-stakes datasets show that the most accuracy AI may not lead to highest team performance and show the benefit of modeling teamwork during training through improvements in expected team utility across datasets, considering parameters such as human skill and the cost of mistakes. We discuss the shortcoming of current optimization approaches beyond well-studied loss functions such as log-loss, and encourage future work on AI optimization problems motivated by human-AI collaboration.

Is the Most Accurate AI the Best Teammate? Optimizing AI for Teamwork

We study a variant of stochastic bandits where the feedback model is specified by a graph. In this setting, after playing an arm, one can observe rewards of not only the played arm but also other arms that are adjacent to the played arm in the graph. Most of the existing work assumes the reward distributions are stationary over time, which, however, is often violated in common scenarios such as recommendation systems and online advertising. To address this limitation, we study stochastic bandits with graph feedback in non-stationary environments and propose algorithms with graph-dependent dynamic regret bounds. When the number of reward distribution changes L is known in advance, one of our algorithms achieves an Ã•(âˆš(Î±LT)) dynamic regret bound. We also develop an adaptive algorithm that can adapt to unknown L and attain an Ã•(âˆš(Î¸LT)) dynamic regret. Here, Î± and Î¸ are some graph-dependent quantities and T is the time horizon.

Stochastic Bandits with Graph Feedback in Non-Stationary Environments

We propose a novel and principled method to learn a nonparametric graph model called graphon, which is defined in an infinite-dimensional space and represents arbitrary-size graphs. 
Based on the weak regularity lemma from the theory of graphons, we leverage a step function to approximate a graphon. 
We show that the cut distance of graphons can be relaxed to the Gromov-Wasserstein distance of their step functions. 
Accordingly, given a set of graphs generated by an underlying graphon, we learn the corresponding step function as the Gromov-Wasserstein barycenter of the given graphs.
Furthermore, we develop several enhancements and extensions of the basic algorithm, e.g., the smoothed Gromov-Wasserstein barycenter for guaranteeing the continuity of the learned graphons and the mixed Gromov-Wasserstein barycenters for learning multiple structured graphons. 
The proposed approach overcomes drawbacks of prior state-of-the-art methods, and outperforms them on both synthetic and real-world data. 
The code is available at https://github.com/HongtengXu/SGWB-Graphon.

Learning Graphons via Structured Gromov-Wasserstein Barycenters

We develop an auto-encoder-type nonlinear dimensionality reduction algorithm to enable the construction of reduced order models of systems governed by convection-dominated nonlinear partial differential equations (PDEs), i.e. snapshots of solutions with large Kolmogorov n-width. Although several existing nonlinear manifold learning methods, such as LLE, ISOMAP, MDS, etc., appear as compelling candidates to reduce the dimensionality of such data, most are not applicable to reduced order modeling of PDEs, because: (i) they typically lack a straightforward mapping from the latent space to the high-dimensional physical space, and (ii) the identified latent variables are often difficult to interpret. In our proposed method, these limitations are overcome by training a low-rank diffeomorphic spatio-temporal grid that registers the output sequence of the PDEs on a non-uniform parameter/time-varying grid, such that the Kolmogorov n-width of the mapped data on the learned grid is minimized. We demonstrate the efficacy and interpretability of our proposed approach on several challenging manufactured computer vision-inspired tasks and physical systems.

Low-Rank Registration Based Manifolds for Convection-Dominated PDEs

The first provably efficient algorithm for learning graph neural networks (GNNs) with one hidden layer for node information convolution is provided in this paper. Two types of GNNs are investigated, depending on whether labels are attached to nodes or graphs. A comprehensive framework for designing and analyzing convergence of GNN training algorithms is developed. The algorithm proposed is applicable to a wide range of activation functions including ReLU, Leaky ReLU, Sigmod, Softplus and Swish. It is shown that the proposed algorithm guarantees a linear convergence rate to the underlying true parameters of GNNs. For both types of GNNs, sample complexity in terms of the number of nodes or the number of graphs is characterized. The impact of feature dimension and GNN structure on the convergence rate is also theoretically characterized. Numerical experiments are further provided to validate our theoretical analysis.

Learning Graph Neural Networks with Approximate Gradient Descent

We introduce Probabilistic Dependency Graphs (PDGs), a new class of directed graphical models.   PDGs can capture inconsistent beliefs in a natural way and are more modular than Bayesian Networks (BNs), in that they make it easier to incorporate new information and restructure the representation.    We show by example how PDGs are an especially natural modeling tool. We provide three semantics for PDGs, each of which can be derived from a scoring function (on joint distributions over the variables in the network) that can be viewed as representing a distribution's incompatibility with the PDG. For the PDG corresponding to a BN, this function is uniquely minimized by the distribution the BN represents, showing that PDG semantics extend BN semantics. We show further that factor graphs and their exponential families can also be faithfully represented as PDGs, while there are significant barriers to modeling a PDG with a factor graph.

Probabilistic Dependency Graphs

Abstract reasoning refers to the ability to analyze information, discover rules at an intangible level, and solve problems in innovative ways. Raven's Progressive Matrices (RPM) test is typically used to examine the capability of abstract reasoning. The subject is asked to identify the correct choice from the answer set to fill the missing panel at the bottom right of RPM (e.g., a 3Ã—3 matrix), following the underlying rules inside the matrix. Recent studies, taking advantage of Convolutional Neural Networks (CNNs), have achieved encouraging progress to accomplish the RPM test. However, they partly ignore necessary inductive biases of RPM solver, such as order sensitivity within each row/column and incremental rule induction. To address this problem, in this paper we propose a Stratified Rule-Aware Network (SRAN) to generate the rule embeddings for two input sequences. Our SRAN learns multiple granularity rule embeddings at different levels, and incrementally integrates the stratified embedding flows through a gated fusion module. With the help of embeddings, a rule similarity metric is applied to guarantee that SRAN can not only be trained using a tuplet loss but also infer the best answer efficiently. We further point out the severe defects existing in the popular RAVEN dataset for RPM test, which prevent from the fair evaluation of the abstract reasoning ability. To fix the defects, we propose an answer set generation algorithm called Attribute Bisection Tree (ABT), forming an improved dataset named Impartial-RAVEN (I-RAVEN for short). Extensive experiments are conducted on both PGM and I-RAVEN datasets, showing that our SRAN outperforms the state-of-the-art models by a considerable margin.

Stratified Rule-Aware Network for Abstract Visual Reasoning

The behaviors of deep neural networks (DNNs) are notoriously resistant to human interpretations. In this paper, we propose Hypergradient Data Relevance Analysis, or HyDRA, which interprets the predictions made by DNNs as effects of their training data. Existing approaches generally estimate data contributions around the final model parameters and ignore how the training data shape the optimization trajectory. By unrolling the hypergradient of test loss w.r.t. the weights of training data, HyDRA assesses the contribution of training data toward test data points throughout the training trajectory. In order to accelerate computation, we remove the Hessian from the calculation and prove that, under moderate conditions, the approximation error is bounded. Corroborating this theoretical claim, empirical results indicate the error is indeed small. In addition, we quantitatively demonstrate that HyDRA outperforms influence functions in accurately estimating data contribution and detecting noisy data labels. The source code is available at https://github.com/cyyever/aaai_hydra.

HyDRA: Hypergradient Data Relevance Analysis for Interpreting Deep Neural Networks

A considerable amount of mobility data has been accumulated due to the proliferation of location-based service. Nevertheless, compared with mobility data from transportation systems like the GPS module in taxis, this kind of data is commonly sparse in terms of individual trajectories in the sense that users do not access mobile services and contribute their data all the time. Consequently, the sparsity inevitably weakens the practical value of the data even it has a high user penetration rate. To solve this problem, we propose a novel attentional neural network-based model, named AttnMove, to densify individual trajectories by recovering unobserved locations at a fine-grained spatial-temporal resolution. To tackle the challenges posed by sparsity, we design various intra- and inter- trajectory attention mechanisms to better model the mobility regularity of users and fully exploit the periodical pattern from long-term history. We evaluate our model on two real-world datasets, and extensive results demonstrate the performance gain compared with the state-of-the-art methods. This also shows that, by providing high-quality mobility data, our model can benefit a variety of mobility-oriented down-stream applications.

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Temporal-Logic-Based Reward Shaping for Continuing Reinforcement Learning Tasks

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Kriging Surrogate Model-Based Design of Ultra-High-Speed Surface-mounted Permanent Magnet Synchronous Motor Considering Stator Iron Loss and Rotor Eddy Current Loss

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